ω-Interpolative Ćirić-Reich-Rus-Type Contractions

In this paper, using the concept of ω-interpolative, we prove some fixed point results for interpolate Ćirić-Reich-Rus-type contraction mappings. We also present some consequences and a useful example

Interpolative Reich-Rus-Ciric and Hardy-Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results

[EN] The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich-Rus-Ciric type contraction and Hardy-Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.Mishra, VN.; Sánchez Ruiz, LM.; Gautam, P.; Verma, S. (2020). Interpolative Reich-Rus-Ciric and Hardy-Rogers Contraction on Quasi-Partial b-Metric Space and Related Fixed Point Results. Mathematics. 8(9):1-11. https://doi.org/10.3390/math8091598S11189Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133-181. doi:10.4064/fm-3-1-133-181Shukla, S. (2013). Partial b-Metric Spaces and Fixed Point Theorems. Mediterranean Journal of Mathematics, 11(2), 703-711. doi:10.1007/s00009-013-0327-4MATTHEWS, S. G. (1994). Partial Metric Topology. Annals of the New York Academy of Sciences, 728(1 General Topol), 183-197. doi:10.1111/j.1749-6632.1994.tb44144.xKARAPINAR, E. (2018). Revisiting the Kannan Type Contractions via Interpolation. Advances in the Theory of Nonlinear Analysis and its Application, 85-87. doi:10.31197/atnaa.431135Reich, S. (1971). Some Remarks Concerning Contraction Mappings. Canadian Mathematical Bulletin, 14(1), 121-124. doi:10.4153/cmb-1971-024-9Hardy, G. E., & Rogers, T. D. (1973). A Generalization of a Fixed Point Theorem of Reich. Canadian Mathematical Bulletin, 16(2), 201-206. doi:10.4153/cmb-1973-036-0Karapinar, E., Agarwal, R., & Aydi, H. (2018). Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces. Mathematics, 6(11), 256. doi:10.3390/math6110256Karapınar, E., Alqahtani, O., & Aydi, H. (2018). On Interpolative Hardy-Rogers Type Contractions. Symmetry, 11(1), 8. doi:10.3390/sym11010008Aydi, H., Karapinar, E., & Roldán López de Hierro, A. (2019). ω-Interpolative Ćirić-Reich-Rus-Type Contractions. Mathematics, 7(1), 57. doi:10.3390/math7010057Debnath, P., & de La Sen, M. de L. (2019). Set-Valued Interpolative Hardy–Rogers and Set-Valued Reich–Rus–Ćirić-Type Contractions in b-Metric Spaces. Mathematics, 7(9), 849. doi:10.3390/math7090849Alqahtani, B., Fulga, A., & Karapınar, E. (2018). Fixed Point Results on Δ-Symmetric Quasi-Metric Space via Simulation Function with an Application to Ulam Stability. Mathematics, 6(10), 208. doi:10.3390/math6100208Aydi, H., Chen, C.-M., & Karapınar, E. (2019). Interpolative Ćirić-Reich-Rus Type Contractions via the Branciari Distance. Mathematics, 7(1), 84. doi:10.3390/math7010084Aydi, H., & Karapinar, E. (2012). A Meir-Keeler common type fixed point theorem on partial metric spaces. Fixed Point Theory and Applications, 2012(1). doi:10.1186/1687-1812-2012-26Ćirić, L., Samet, B., Aydi, H., & Vetro, C. (2011). Common fixed points of generalized contractions on partial metric spaces and an application. Applied Mathematics and Computation, 218(6), 2398-2406. doi:10.1016/j.amc.2011.07.005Karapınar, E., Chi, K. P., & Thanh, T. D. (2012). A Generalization of Ćirić Quasicontractions. Abstract and Applied Analysis, 2012, 1-9. doi:10.1155/2012/518734Mlaiki, N., Abodayeh, K., Aydi, H., Abdeljawad, T., & Abuloha, M. (2018). Rectangular Metric-Like Type Spaces and Related Fixed Points. Journal of Mathematics, 2018, 1-7. doi:10.1155/2018/3581768Gupta, A., & Gautam, P. (2016). Topological Structure of Quasi-Partial b-Metric Spaces. International Journal of Pure Mathematical Sciences, 17, 8-18. doi:10.18052/www.scipress.com/ijpms.17.8Gupta, A., & Gautam, P. (2015). Quasi-partial b-metric spaces and some related fixed point theorems. Fixed Point Theory and Applications, 2015(1). doi:10.1186/s13663-015-0260-

From interpolative contractive mappings to generalized Ciric-quasi contraction mappings

[EN] In this article we consider a restricted version of Ciric-quasi contraction mapping for showing that this mapping generalizes several known interpolative type contractive mappings. Also here we introduce the concept of interpolative strictly contractive type mapping T and prove a fixed point theorem for such mapping over a T-orbitally compact metric space. Some examples are given in support of our established results. Finally we give an observation regarding (λ, α, β)-interpolative Kannan contractions introduced by Gaba et al.First and second authors acknowledge financial support awarded by the Council of Scientific and Industrial Research, New Delhi, India, through research fellowship for carrying out research work leading to the preparation of this manuscript.Roy, K.; Panja, S. (2021). From interpolative contractive mappings to generalized Ciric-quasi contraction mappings. Applied General Topology. 22(1):109-120. https://doi.org/10.4995/agt.2021.14045OJS109120221C. B. Ampadu, Some fixed point theory results for the interpolative Berinde weak operator, Earthline Journal of Mathematical Sciences 4 no. 2 (2020), 253-271. https://doi.org/10.34198/ejms.4220.253271S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181L. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45, no. 2 (1974), 267-273. https://doi.org/10.2307/2040075H. Garai, L. K. Dey and T. Senapati, On Kannan-type contractive mappings, Numerical Functional Analysis and Optimization 39, no. 13 (2018), 1466-1476. https://doi.org/10.1080/01630563.2018.1485157L. B. Ciric, Generalized contractions and fixed-point theorems, Publ. Inst. Math. 12 (1971), 19-26.Y. U. Gaba and E. Karapinar, A new approach to the interpolative contractions, Axioms 8, no. 4 (2019), 110. https://doi.org/10.3390/axioms8040110E. Karapinar, Revisiting the Kannan type contractions via interpolation. Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85-87. https://doi.org/10.31197/atnaa.431135E. Karapinar, R. P. Agarwal and H. Aydi, Interpolative Reich-Rus-Ciric type contractions on partial metric spaces, Mathematics 6, no. 11 (2018), 256. https://doi.org/10.3390/math6110256E. Karapinar, O. Alqahtani and H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry 11, no. 1 (2018), 8. https://doi.org/10.3390/sym11010008A. F. Roldán López de Hierro, E. Karapinar and A. Fulga, Multiparametric contractions and related Hardy-Roger type fixed point theorems, Mathematics 8, no. 6 (2020), 957. https://doi.org/10.3390/math806095

On Some Novel Fixed Point Results for Generalized F-Contractions in b-Metric-Like Spaces with Application

The focus of our work is on the most recent results in fixed point theory related to contractive mappings.We describe variants of (s, q, φ, F)-contractions that expand, supplement and unify an important work widely discussed in the literature, based on existing classes of interpolative and F-contractions. In particular, a large class of contractions in terms of s, q, φ and F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces. The main result in our paper is that (s, q, φ, F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous. As an application of our results, we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations

A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics

On Interpolative Hardy-Rogers Type Contractions

By using an interpolative approach, we recognize the Hardy-Rogers fixed point theorem in the class of metric spaces. The obtained result is supported by some examples. We also give the partial metric case, according to our result