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In this paper, we introduce the concept of generalized asymmetric metric spaces and we prove some fixed point theorems in the setting of this metric spaces and also some illustrative examples are given. The presented results generalize and improve several results of the topics in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the iterations of strongly (asymptotic) quasi ø-nonexpansive mappings in Banach spaces. First, we prove weak convergence of the generated sequence to a common fixed point of an infinite family of strongly asymptotic quasi ø-nonexpansive mappings. Next we prove strong convergence of the generated sequence by an additional assumption. In the sequel, invoke of Halpern regularization method, we prove strong convergence of the generated sequence to a common fixed point of the family of mappings without any extra conditions. Finally, we give some applications of our main results in convex minimization and equilibrium problems and present numerical examples to illustrate and support them. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new concept of contraction called F-Khan-contractions and prove a fixed point theorem concerning this contraction which generalizes the results announced by Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste., 8 (1976), 69-72], Fisher [B. Fisher, Riv. Math. Univ. Parma., 4 (1978), 135-137], and Piri et al. [H. Piri, S. Rahrovi, P. Kumam, J. Math. Computer Sci., 17 (2017), 76-83]. An example and application for the solution of certain integral equations are given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce hybrid pseudo-viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family and left amenable semigroup of non-expansive mappings in the frame work of Hilbert spaces. Our goal is to prove a result of strong convergence for hybrid pseudo-viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non-expansive mappings. The results presented in this paper can be treated as an extension and improvement of the corresponding results announced by Ceng et al. [L.C. Ceng, Q.H. Ansari, and J.C. Yao, Hybrid pseudo-viscosity approximation schemes for equilibrium problems and fixed point problems of infinitely many non-expansive mappings, Nonlinear Analysis 4 (2010) 743–754] and many others. [Copyright &y& Elsevier]