Let T : K → H be a mapping from a nonempty closed convex subset K of a finitedimensional Hilbert space H into H . Let f : K → R be proper, convex, and lower semicontinuous on K and let h : K → R be continuously Frećhet-differentiable on K with h′ (gradient of h), α-strongly monotone, and β-Lipschitz continuous on K . Then the sequence {xk} generated by the general auxiliary problem principle co...

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we introduce generalized additive mappings of Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative additive mappings.

This paper studies the convergence of fixed points for Garsia-Falset generalized nonexpansive mappings. First, it investigates weak and strong results mappings using Temir-Korkut iteration in uniformly convex Banach spaces. then exemplifies mappings, which exceed class Suzuki Moreover, numerically compares this iteration's speed with well-known Thakur approximating point mapping. The show that ...

In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is version recently developed mappings. We establish some elementary properties fixed point existence results for these Moreover, a M-iterative scheme proposed approximating points mappings in weak strong senses. Using an example, also show that converges faster as compared to many oth...

in this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy m-complete metric spaces. we also give an affirmative partial answer to a question posed by wardowski [d. wardowski, fuzzy contractive mappings and fixed points in fuzzy metric spaces, fuzzy set syst., {bf 222}(2013), 108-114].some examples are also g...