Fixed point theorems for nonlinear contractions with applications to iterated function systems

[EN] We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.Pant, R. (2018). Fixed point theorems for nonlinear contractions with applications to iterated function systems. Applied General Topology. 19(1):163-172. doi:10.4995/agt.2018.7918SWORD16317219

Some fixed point results for enriched nonexpansive type mappings in Banach spaces

[EN] In this paper, we introduce two new classes of nonlinear mappings and present some new existence and convergence theorems for these mappings in Banach spaces. More precisely, we employ the Krasnosel'skii iterative method to obtain fixed points of Suzuki-enriched nonexpansive mappings under different conditions. Moreover, we approximate the fixed point of enriched-quasinonexpansive mappings via Ishikawa iterative method. The first author acknowledges the support from the GES 4.0 fellowship, University of Johannesburg, South Africa.Shukla, R.; Pant, R. (2022). Some fixed point results for enriched nonexpansive type mappings in Banach spaces. Applied General Topology. 23(1):31-43. https://doi.org/10.4995/agt.2022.16165314323

Fixed point theorems for a new class of nonexpansive mappings

[EN] We consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results.Pant, R.; Shukla, R. (2022). Fixed point theorems for a new class of nonexpansive mappings. Applied General Topology. 23(2):377-390. https://doi.org/10.4995/agt.2022.1735937739023

Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces

[EN] We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappingss in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed.Pant, R.; Pandey, R. (2019). Existence and convergence results for a class of nonexpansive type mappings in hyperbolic spaces. Applied General Topology. 20(1):281-295. https://doi.org/10.4995/agt.2019.11057SWORD281295201M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesnik 66, no. 2 (2014), 223-234.R. P. Agarwal, D. O'Regan and D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79.A. Amini-Harandi, M. Fakhar and H. R. Hajisharifi, Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces, J. Fixed Point Theory Appl. 18, no. 3 (2016), 601-607. https://doi.org/10.1007/s11784-016-0310-3K. Aoyama and F. Kohsaka, Fixed point theorem for α-nonexpansive mappings in Banach spaces, Nonlinear Anal. 74, no. 13 (2011), 4387-4391. https://doi.org/10.1016/j.na.2011.03.057B. A. Bin Dehaish and M. A. Khamsi, Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016:20 (2016). https://doi.org/10.1186/s13663-016-0505-8H. Busemann, Spaces with non-positive curvature, Acta Math. 80 (1948), 259-310. https://doi.org/10.1007/BF02393651T. Butsan, S. Dhompongsa and W. Takahashi, A fixed point theorem for pointwise eventually nonexpansive mappings in nearly uniformly convex Banach spaces, Nonlinear Anal. 74, no. 5 (2011), 1694-1701. https://doi.org/10.1016/j.na.2010.10.041J. García-Falset, E. Llorens-Fuster and T. Suzuki, Fixed point theory for a class of generalized nonexpansive mappings, J. Math. Anal. Appl. 375, no. 1 (2011), 185-195. https://doi.org/10.1016/j.jmaa.2010.08.069H. Fukhar-ud-din and M. A. Khamsi, Approximating common fixed points in hyperbolic spaces, Fixed Point Theory Appl. 2014:113 (2014). https://doi.org/10.1186/1687-1812-2014-113K. Goebel and M. Japón-Pineda, A new type of nonexpansiveness, Proceedings of 8-th international conference on fixed point theory and applications, Chiang Mai, 2007.K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171-174. https://doi.org/10.1090/S0002-9939-1972-0298500-3K. Goebel, T. Sekowski and A. Stachura, Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball, Nonlinear Anal. 4, no. 5 (1980), 1011-1021. https://doi.org/10.1016/0362-546X(80)90012-7K. Goebel and W. A. Kirk, Iteration processes for nonexpansive mappings, Topological methods in nonlinear functional analysis (Toronto, Ont., 1982), Contemp. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1983, pp. 115-123. https://doi.org/10.1090/conm/021/729507K. Goebel and S. Reich, Uniform convexity, hyperbolic geometry, and nonexpansive mappings, Monographs and Textbooks in Pure and Applied Mathematics, vol. 83, Marcel Dekker, Inc., New York, 1984. https://doi.org/10.1112/blms/17.3.293M. Gregus, Jr., A fixed point theorem in Banach space, Boll. Un. Mat. Ital. A (5) 17, no. 1 (1980), 193-198.M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, english ed., Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2007, Based on the 1981 French original, With appendices by M. Katz, P. Pansu and S. Semmes, Translated from the French by Sean Michael Bates. https://doi.org/10.1007/978-0-8176-4583-0B. Gunduz and S. Akbulut, Strong convergence of an explicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces, Miskolc Math. Notes 14 (2013), no. 3, 905-913. https://doi.org/10.18514/mmn.2013.641S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59, no. 1 (1976), 65-71. https://doi.org/10.1090/S0002-9939-1976-0412909-XM. A. Khamsi, On metric spaces with uniform normal structure, Proc. Amer. Math. Soc. 106, no. 3 (1989), 723-726. https://doi.org/10.1090/S0002-9939-1989-0972234-4M. A. Khamsi and A. R. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. 74 (2011), no. 12, 4036-4045. https://doi.org/10.1016/j.na.2011.03.034S. H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory Appl. 2013:69 (2013), 10. https://doi.org/10.1186/1687-1812-2013-69S. H. Khan, D. Agbebaku and M. Abbas, Three step iteration process for two multivalued nonexpansive maps in hyperbolic spaces, J. Math. Ext. 10, no. 4 (2016), 87-109.S. H. Khan and M. Abbas, Common fixed point results for a Banach operator pair in CAT(0) spaces with applications, Commun. Fac. Sci. Univ. Ank. S'{e}r. A1 Math. Stat. 66 (2017), no. 2, 195-204. https://doi.org/10.1501/commua1_0000000811S. H. Khan, M. Abbas and T. Nazir, Existence and approximation results for skc mappings in busemann spaces, Waves Wavelets Fractals Adv. Anal. 3 (2017), 48-60.https://doi.org/10.1515/wwfaa-2017-0005S. H. Khan and H. Fukhar-ud din, Convergence theorems for two finite families of some generalized nonexpansive mappings in hyperbolic spaces, J. Nonlinear Sci. Appl. 10, no. 2 (2017), 734-743. https://doi.org/10.22436/jnsa.010.02.34A. R. Khan, H. Fukhar-ud din and M. A. A. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl. 2012:54 (2012), 12. https://doi.org/10.1186/1687-1812-2012-54W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346. https://doi.org/10.1007/BF02757136W. A. Kirk, Fixed point theory for nonexpansive mappings, Fixed point theory (Sherbrooke, Que., 1980), Lecture Notes in Math., vol. 886, Springer, Berlin-New York, 1981, pp. 484-505. https://doi.org/10.1007/bfb0092201W. A. Kirk, Fixed point theorems in CAT(0) spaces and R-trees, Fixed Point Theory Appl. 2004:4 (2004), 309-316. https://doi.org/10.1155/S1687182004406081W. A. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal. 68, no. 12 (2008), 3689-3696. https://doi.org/10.1016/j.na.2007.04.011U. Kohlenbach, Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. 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Ann. 100, no. 1 (1928), 75-163. https://doi.org/10.1007/BF01448840S. A. Naimpally, K. L. Singh and J. H. M. Whitfield, Fixed points in convex metric spaces, Math. Japon. 29, no. 4 (1984), 585-597.A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory Appl. (2010), Art. ID 458265, 19. https://doi.org/10.1155/2010/458265M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251, no. 1 (2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042R. Pant and R. Shukla, Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optim. 38, no. 2 (2017), 248-266. https://doi.org/10.1080/01630563.2016.1276075S. Reich and I. Shafrir, Nonexpansive iterations in hyperbolic spaces, Nonlinear Anal. 15 (1990), no. 6, 537-558. https://doi.org/10.1016/0362-546x(90)90058-oRitika and S. H. 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Fixed Point Theorems for Nonexpansive Type Mappings in Banach Spaces

In this paper, we present some fixed point results for a class of nonexpansive type and α-Krasnosel’skiĭ mappings. Moreover, we present some convergence results for one parameter nonexpansive type semigroups. Some non-trivial examples have been presented to illustrate facts.The authors thanks the Basque Government for its support through Grant IT1207-19

Induced Size Effects Of Gd3+ ions Doping On Structural And Magnetic Properties Of Ni-Zn Ferrite Nanoparticles

Gd3+ ions substituted in Ni0.5Zn0.5GdxFe2-xO4 (where x = 0.1, 0.2, 0.3) ferrite nanoparticles in the size range from 15 to 25 nm were prepared by chemical method. The effect of Gd3+ ions in spinel structure in correlation to structural and magnetic properties have been studied in detail using XRD, HRTEM and EPR techniques. The spin resonance confirms the ferromagnetic behaviour of these nanoparticles and higher order of dipolar-dipolar interaction. On increasing Gd3+ ions concentrations, the super exchange interaction i.e. increase in movement of electron among Gd3+ - O - Fe3+ in the core group and the spin biasing in the glass layer has been interpreted. The decrease in ‘g’ value and increase in relaxation time is well correlated with the change of particle size on different concentrations of Gd3+ ions in Ni-Zn ferrite

The Stability and Well-Posedness of Fixed Points for Relation-Theoretic Multi-Valued Maps

The purpose of this study is to present fixed-point results for Suzuki-type multi-valued maps using relation theory. We examine a range of implications that arise from our primary discovery. Furthermore, we present two substantial cases that illustrate the importance of our main theorem. In addition, we examine the stability of fixed-point sets for multi-valued maps and the concept of well-posedness. We present an application to a specific functional equation which arises in dynamic programming

Approximating Solutions of Matrix Equations via Fixed Point Techniques

The principal goal of this work is to investigate new sufficient conditions for the existence and convergence of positive definite solutions to certain classes of matrix equations. Under specific assumptions, the basic tool in our study is a monotone mapping, which admits a unique fixed point in the setting of a partially ordered Banach space. To estimate solutions to these matrix equations, we use the Krasnosel’skiĭ iterative technique. We also discuss some useful examples to illustrate our results.The authors thank the Basque Government for its support through Grant IT1207-19

Efficacy of maternal B-12 supplementation in vegetarian women for improving infant neurodevelopment: protocol for the MATCOBIND multicentre, double-blind, randomised controlled trial

INTRODUCTION: Vitamin B12 deficiency is widely prevalent across many low- and middle-income countries, especially where the diet is low in animal sources. While many observational studies show associations between B12 deficiency in pregnancy and infant cognitive function (including memory, language and motor skills), evidence from clinical trials is sparse and inconclusive. METHODS AND ANALYSIS: This double-blind, multicentre, randomised controlled trial will enrol 720 vegetarian pregnant women in their first trimester from antenatal clinics at two hospitals (one in India and one in Nepal). Eligible mothers who give written consent will be randomised to receive either 250 mcg methylcobalamin or 50 mcg (quasi control), from enrolment to 6 months post-partum, given as an oral daily capsule. All mothers and their infants will continue to receive standard clinical care. The primary trial outcome is the offspring's neurodevelopment status at 9 months of age, assessed using the Development Assessment Scale of Indian Infants. Secondary outcomes include the infant's biochemical B12 status at age 9 months and maternal biochemical B12 status in the first and third trimesters. Maternal biochemical B12 status will also be assessed in the first trimester. Modification of association by a priori identified factors will also be explored. ETHICAL CONSIDERATIONS AND DISSEMINATION: The study protocol has been approved by ethical committees at each study site (India and Nepal) and at University College London, UK. The study results will be disseminated to healthcare professionals and academics globally via conferences, presentations and publications. Researchers at each study site will share results with participants during their follow-up visits.Trial registration numberCTRI/2018/07/015048 (Clinical Trial Registry of India); NCT04083560 (ClinicalTrials.gov)