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Local generalizations of Banach’s contraction map** principle
In this paper we prove certain generalized local versions of the Banach’s contraction map** principle. We give a comparison amongst these results...
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A fixed point theorem for Proinov map**s with a contractive iterate
In this paper, we consider the fixed point theorem for Proinov map**s with a contractive iterate at a point. In other words, we combine and unify...
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Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. Moreover,...
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Uniqueness of a nonlinear integro-differential equation with nonlocal boundary condition and variable coefficients
This paper studies the uniqueness of solutions to a two-term nonlinear fractional integro-differential equation with nonlocal boundary condition and...
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An overview of the emergence of weaker continuity notions, various classes of contractive map**s and related fixed point theorems
This paper presents an overview that aims to discuss a brief historical account of the development through the definitions and comparison of weaker...
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The Banach Fixed Point Theorem: selected topics from its hundred-year history
On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ...
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A new contractive condition related to Rhoades’s open question
An open problem proposed by Rhoades is the following. Is there a contractive condition which guarantees the existence of a fixed point, but does not...
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On Common Fixed Point Results for Integral Type Contractive Conditions in \(\varOmega \) -Metric Spaces and Application to Integral Equations
Sedghi and Dung (Fixed point theorems on \(\varOmega \)...
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Best Proximity Points for Some Multivalued Contractive Map**s
Best proximity point theorems provide assurance to the existence of approximate solutions to some particular equations of the type...
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Fixed-point theorems of \({F}^{\star}- ( \psi,\phi )\) integral-type contractive conditions on \(1_{E}\)-complete multiplicative partial cone metric spaces over Banach algebras and applications
In this paper, we introduce some user-friendly versions of integral-type fixed-point results and give some modifications of the classical Banach...
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Existence and stability results for fractional boundary value problems in Banach spaces
In this work, the existence and uniqueness of solutions for nonlinear fractional jerk type problem with nonlocal boundary conditions are investigated...
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Metric Fixed Point Theory
The aim of this chapter is to give a brief history of metric fixed point theory. In this section, we discuss the pioneer metric fixed point theorem...
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Fixed Point Results for the Fractional Nonlinear Problem with Integral Boundary Condition
In this article, we study an integral boundary condition problem. In fact, we consider a new nonlinear fractional integro-differential equation with...
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Results on Hardy–Rogers Contraction
With a proper metrizability approach that preserves completeness of a metric space, Hardy–Rogers contraction may be observed as a Banach contraction....
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A Careful Retrospection of Metric Spaces and Contraction Map**s with Computer Simulation
This chapter aims to provide a straightforward layout of the work done on contraction map**s, that play an indispensable role in the fixed-point...
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Basic Fixed Point Theorems in Metric Spaces
This chapter is a review work on the development of metric fixed point theory. It begins with the description of Banach’s Contraction Map**...
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Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations
We study sequential fractional pantograph q -differential equations. We establish the uniqueness of solutions via Banach’s contraction map**...
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Remarks on a fractional nonlinear partial integro-differential equation via the new generalized multivariate Mittag-Leffler function
Introducing a new generalized multivariate Mittag-Leffler function which is a generalization of the multivariate Mittag-Leffler function, we derive a...
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On the existence, uniqueness, stability, and numerical aspects for a novel mathematical model of HIV/AIDS transmission by a fractal fractional order derivative
In this study, we explore a mathematical model of the transmission of HIV/AIDS. The model incorporates a fractal fractional order derivative with a...
