The well-known Banach’s fixed point theorem asserts that if D = X, f is contractive and (X, d) is complete, then f has a unique fixed point in X. In nonlinear analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been investigated deeply. The Banach contraction principle [1] is one of the initial and crucial results in thi...

The idea of enriched mappings in normed spaces is relatively a newer idea. In this paper, we initiate the study modular function spaces. We first introduce concepts ρ-contractions and ρ-Kannan then establish some Banach Contraction Principle type theorems for existence fixed points such setting. Our results are generalizations corresponding from to those contractions ρ-contractions. make ever a...

The convergence of a Presić type k-step iterative method for a new class of operators f : Xk → X satisfying a general Presić type contraction condition is proved. Our result is completing an existing list of Presić type iteration methods, see [Rus I. A., An iterative method for the solution of the equation x = f(x, . . . , x), Rev. Anal. Numer. Theor. Approx., 10(1) (1981), 95–100] and the rece...

We introduce the class of contraction algebras in which the algebra of infinite and finite terms is free over the set of variables. We develop a general theory of systems of equations at the level of categories in close connection with the Banach Principle of Contraction. Two applications of this theory are given. The first is the case of regular systems of equations with arbitrary terms. The s...

In this article, we introduce the concept of intuitionistic fuzzy double controlled metric spaces that generalizes b-metric spaces. For purpose, two noncomparable functions are used in triangle inequalities. We generalize concepts Banach contraction principle and contractive mappings by giving authentic proof these sense To validate superiority results, examples imparted. A possible application...

In this study we shall obtain some sufficient conditions for the existence of positive solutions variable coefficient nonlinear second-order neutral differential equation with distributed deviating arguments. For different cases range p(t) by using Banach contraction principle will give nonoscillatory equation. With purpose use fixpoint theorem. At end research, there is an example that meets h...

The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability ψ-Caputo fractional neutral delay differential system. We use ψ-delayed perturbation Mitttag–Leffler matrix function Banach contraction principle examine Ulam–Hyers our considered formulate Grammian establish results linear fractonal Further, we employ fixed-point technique Krasnoselskii’s type sufficient ...

     Dx(t) + f(t, x(t), x(t)) = 0, t ∈ (0, 1), x(0) = ∫ 1 0 g0(s, x(s))ds, x(1) = ∫ 1 0 g1(s, x(s))ds, x(0) = 0, k = 2, 3, · · · , [α]− 1. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of solutions are dependent on the order α.