Results 71 to 80 of about 5,440 (186)

Condensing Operators in Busemann Convex Metric Spaces With Applications to Hammerstein Integral Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this article, we introduce a new class of cyclic and noncyclic condensing operators that extend the notion of condensing mappings previously proposed by Gabeleh and Markin (M. Gabeleh and J. Markin, Optimum solutions for a system of differential equations via measure of noncompactness, Indagationes Mathematicae, 29(3) [2018], 895–906).
A. Pradhan, M. Gabeleh, D. K. Patel, S. P. Moshokoa, Shikha Binwal   +4 more
wiley   +1 more source

On extremal nonexpansive mappings

Zeitschrift für Analysis und ihre Anwendungen
We study the extremality of nonexpansive mappings on a non-empty bounded, closed, and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces, including Banach spaces with the Radon–Nikodym property and all
Christian Bargetz, Michael Dymond, Katriin Pirk   +2 more
openaire   +3 more sources

Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces

Abstract and Applied Analysis, 2011
We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings {Tn} in convex metric spaces. We prove that the sequence {xn} generated by the proposed iteration is an approximating fixed point sequence of a ...
Withun Phuengrattana, Suthep Suantai
doaj   +1 more source

Controlled Metric Space and Fixed Point Theorems for Jaggi–Suzuki–Type Hybrid Contraction

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new notion of generalized Jaggi–Suzuki–type hybrid contraction in the setting of controlled metric space and prove some fixed point theorems by making use of the same. A suitable example is also provided to prove the validity of our results.
Swati Parashar, Manoj Kumar, Pankaj Kumar, Rahul Shukla, Birendra Nath Mandal   +4 more
wiley   +1 more source

On directionally nonexpansive mappings

European Journal of Mathematics
AbstractIn 2000, W.A. Kirk introduced the concept of directionally nonexpansive mappings. Here, we present a more comprehensive study of this class of mappings, including a fixed-point result for them. We further present a class of mappings, properly containing the directionally nonexpansive ones, for which Kirk’s theorem still holds.
openaire   +1 more source

Fixed Point Theorems on Controlled Orthogonal δ‐Metric‐Type Spaces and Applications to Fractional Integrals

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this article, we introduce a notion of controlled orthogonal δ‐metric‐type spaces with an example. Further, we prove a contraction theorem and a generalized fixed point theorem in controlled orthogonal δ‐metric‐type spaces. Finally, we illustrate two applications of the obtained fixed point results on the Atangana–Baleanu fractional integrals and ...
Benitha Wises Samuel, Gunaseelan Mani, Purushothaman Ganesh, Sabri T. M. Thabet, Imed Kedim, Samuel Nicolay   +5 more
wiley   +1 more source

Investigating Nonlinear Activation Mechanism Through Fixed‐Circle Theorems of Enriched Multivalued Bilateral‐Type Contractions

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this article, we present new results addressing the fixed‐circle and fixed‐disc problems through modification of the multivalued bilateral Jaggi‐type and Dass–Gupta‐type contractions. Furthermore, we demonstrate the application of these theorems to the nonlinear activation mechanism used in neural networks.
Saima Kanwal, Naeem Saleem, Ali Althobaiti, Samuel Nicolay   +3 more
wiley   +1 more source

Strong convergence theorems for a sequence of nonexpansive mappings with gauge functions

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013
In this paper, we first prove a path convergence theorem for a nonexpansive mapping in a reflexive and strictly convex Banach space which has a uniformly Gˆateaux differentiable norm and admits the duality mapping jφ, where φ is a gauge function on [0,∞).
Cholamjiak Prasit, Je Cho Yeol, Suantai Suthep   +2 more
doaj   +1 more source

On the Monotone Variational Inclusion Problems: A New Algorithm‐Based Modified Splitting Approach

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this paper, we introduce and analyze an inertial viscosity forward–backward splitting approach. We approximate a common solution of the monotone variational inclusion problem by using the demicontractive mapping in a real Hilbert space. It is shown that the sequence produced by our suggested algorithm has a strong convergence to a solution obtained ...
Uzoamaka A. Ezeafulukwe, George B. Akuchu, Sina Etemad, Austine E. Ofem, Godwin C. Ugwunnadi, Zaher Mundher Yaseen, Xian-Ming Gu   +6 more
wiley   +1 more source

Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces

Abstract and Applied Analysis, 2010
Let E be a real Banach space which is uniformly smooth and uniformly convex. Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction. If E admits weakly sequentially continuous duality mapping
Yekini Shehu, Jerry N. Ezeora
doaj   +1 more source