There are a lot of generalizations of the Banach contraction mapping principle in the literature. One of the most interesting of them is the result of Khan et al. 1 . They addressed a new category of fixed point problems for a single self-map with the help of a control function which they called an altering distance function. A function φ : 0,∞ → 0,∞ is called an altering distance function if φ...

This paper presents a new class of boundary value problems integrodifferential fractional equations different order equipped with coupled anti-periodic and nonlocal integral conditions. We prove the existence uniqueness criteria solutions by using Leray-Schauder alternative Banach contraction mapping principle. Examples are constructed for illustration our results.

If (X, d) is a complete metric space and T : X → X is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of T starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader...

In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

for all x, y ∈ X . Then there exists a unique fixed point x0 ∈ X of T . This theorem, called the Banach contraction principle, is a forceful tool in nonlinear analysis. This principle has many applications and is extended by several authors: Caristi [2], Edelstein [5], Ekeland [6, 7], Meir and Keeler [14], Nadler [15], and others. These theorems are also extended; see [4, 9, 10, 13, 23, 25, 26,...

This article aims at investigating stability properties for a class of discrete fractional equations with anti-periodic boundary conditions order \(\delta=(3,4]\). Utilizing Contraction mapping principle and fixed point theorem due to Brouwer, new criteria the uniqueness existence solutions are developed two types Ulam analysed. The theoretical outcomes corroborated examples.

Branciari [1] obtained a fixed point result for a single mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality. The second author [3] proved two fixed point theorems involving more general contractive conditions. In this paper, we establish a general principle, which makes it possible to prove many fixed point theorems for a pair of maps of integral ty...

The solution to a sequential fractional differential equation with affine periodic boundary value conditions is investigated in this paper. existence theorem of established by means the Leray–Schauder fixed point and Krasnoselskii theorem. What more, uniqueness demonstrated via Banach contraction mapping principle. In order illustrate main results, two examples are listed.

in this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by gregori and sapena [v. gregori, a. sapena, on xed-point the- orems in fuzzy metric spaces, fuzzy sets and systems, 125 (2002), 245-252].