Common new fixed point results on b-cone Banach spaces over Banach algebras

[EN] Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of φ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by using φ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions and following their work with introducing two mappings T and S we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.Afshari, H.; Shojaat, H.; Fulga, A. (2022). Common new fixed point results on b-cone Banach spaces over Banach algebras. Applied General Topology. 23(1):145-156. https://doi.org/10.4995/agt.2022.15571OJS14515623

Fixed point theory in the setting of (α,β,ψ,φ)-interpolative contractions

The authors thank their universities. A.F. Roldan Lopez de Hierro is grateful to Junta de Andalucia by project FQM-365 of the Andalusian CICYE and to Ministerio de Ciencia e Innovacion by project PID2020-119478GB-I00.In this manuscript we introduce the notion of (α,β,ψ,φ)-interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.Junta de Andalucia FQM-365 PID2020-119478GB-I0

A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces

[EN] In this paper we consider a kind of Geraghty contractions by using mw-distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained.This research was partially supported by the Spanish Ministry of Science, Innovation and Universities. Grant number PGC2018-095709-B-C21 and AEI/FEDER, UE funds.Alegre Gil, MC.; Fulga, A.; Karapinar, E.; Tirado Peláez, P. (2020). A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces. Mathematics. 8(9):1-10. https://doi.org/10.3390/math8091437S11089Geraghty, M. A. (1973). On contractive mappings. Proceedings of the American Mathematical Society, 40(2), 604-604. doi:10.1090/s0002-9939-1973-0334176-5Gupta, V., Shatanawi, W., & Mani, N. (2016). Fixed point theorems for $$(\psi , \beta )$$ ( ψ , β ) -Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations. Journal of Fixed Point Theory and Applications, 19(2), 1251-1267. doi:10.1007/s11784-016-0303-2Cho, S.-H., Bae, J.-S., & Karapınar, E. (2013). Fixed point theorems for α-Geraghty contraction type maps in metric spaces. Fixed Point Theory and Applications, 2013(1). doi:10.1186/1687-1812-2013-329Alegre, C., & Marín, J. (2016). Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces. Topology and its Applications, 203, 32-41. doi:10.1016/j.topol.2015.12.073Alegre Gil, C., Karapınar, E., Marín Molina, J., & Tirado Peláez, P. (2019). Revisiting Bianchini and Grandolfi Theorem in the Context of Modified $$\omega$$-Distances. Results in Mathematics, 74(4). doi:10.1007/s00025-019-1074-zAlegre, C., Marín, J., & Romaguera, S. (2014). A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces. Fixed Point Theory and Applications, 2014(1). doi:10.1186/1687-1812-2014-40Park, S. (2000). On generalizations of the Ekeland-type variational principles. Nonlinear Analysis: Theory, Methods & Applications, 39(7), 881-889. doi:10.1016/s0362-546x(98)00253-

Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Very recently, Proinov introduced a great family of contractions in the setting of complete metric spaces that has attracted the attention of many researchers because of the very weak conditions that are assumed on the involved functions. Inspired by Proinov’s results, in this paper, we introduce a new class of contractions in the setting of fuzzy metric spaces (in the sense of George and Veeramani) that are able to translate to this framework the best advantages of the abovementioned auxiliary functions. Accordingly, we present some results about the existence and uniqueness of fixed points for this class of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces

Proinov type contractions on dislocated b-metric spaces

The authors thank their universities. The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group no. RG-1437-037. A.F. Roldán López de Hierro is grateful to Project TIN2017-89517-P of Ministerio de Economía, Industria y Competitividad and also to Junta de Andalucía by project FQM-365 of the Andalusian CICYE.In this paper, we improve the Proinov theorem by adding certain rational expressions to the definition of the corresponding contractions. After that, we prove fixed point theorems for these modified Proinov contractions in the framework of dislocated b-metric spaces. We show some illustrative examples to indicate the validity of the main results.King Saud University RG-1437-037Ministerio de Economia, Industria y Competitividad TIN2017-89517-PJunta de Andalucia FQM-36

Heart disease detection using inertial Mann relaxed CQ algorithms for split feasibility problems

This study investigates the weak convergence of the sequences generated by the inertial relaxed $CQ$ algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed $CQ$ algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score

Some Results on S-Contractions of Type E

In this manuscript, we consider the compositions of simulation functions and E-contraction in the setting of a complete metric space. We investigate the existence and uniqueness of a fixed point for this composite form. We give some illustrative examples and provide an application

An admissible Hybrid contraction with an Ulam type stability

In this manuscript, we introduce a new hybrid contraction that unify several nonlinear and linear contractions in the set-up of a complete metric space. We present an example to indicate the genuine of the proved result. In addition, we consider Ulam type stability and well-posedness for this new hybrid contraction

A Hybrid Contraction that Involves Jaggi Type

In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction in separate theorems. We consider a solution to certain fractional differential equations as an application of the given results. In addition, we provide an example to indicate the genuineness of the given results

Discussions on Proinov-Cb-Contraction Mapping on b-Metric Space

In the present paper, we introduce the notion of Proinov-Cb-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples