Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

Episodes in Metric Fixed Point Theory related to F. E. Browder

Sehie Park — Sat, 01 Jun 2024 00:00:00 +0700

F.E. Browder in 1979 posed a fixed point theorem of great generality
and complexity such that a large part of literature on contractive type of
mapscan be subsumed under an intuitive and simple mode of argument.
Immediately after, several researchers found better theorems than his
result. Since then only a few authors quote his theorem. However, until
recently, certain minor papers related to Browder's aim.Our aim in this
paper is to introduce the contents of them.

Best Proximity Point and Fixed Point Theorems in Complex Valued Rectangular b-Metric Spaces

Warinsinee Chantakun, Tadchai Yuying, Supavinee Sattayaporn — Sat, 01 Jun 2024 00:00:00 +0700

The aim of this paper, by using the concept of continuity of which satisfying
and to defined some contraction condition of T introduced by G. Meena [12], we prove the unique
best proximity point of A and fixed point of T in complex valued rectangular b-metric space. Our results
extend and improve the results of G. Meena [12], and many others.

FIXED POINT THEOREMS FOR ĆIRIĆ’S QUASICONTRACTION IN GENERALIZED COMPLEX VALUED METRIC SPACES

Tadchai Yuying, Issara Inchan, Kiattisak Rattanaseeha — Sat, 01 Jun 2024 00:00:00 +0700

In this work, we introduce some property of the generalized complex valued
metric space and we extend some fixed point results thai is Ćirić’s fixed point theorem.
Some are recover various complex valued metric space and complex valued b-metric space.
Our results extended and improve some results of Mohamed Jleli and Bessem Samet [14].

SOLVABILITY OF EQUATIONS INVOLVING PERTURBATIONS OF m-ACCRETIVE OPERATORS IN BANACH SPACES

Masashi Toyoda, Yukio Takeuchi — Sat, 01 Jun 2024 00:00:00 +0700

It is purpose of this paper to give several results for the solvability of the
equation p ∈ Ax + Sx, where A is an m-accretive operator on a Banach space E and S
is a mapping on a subset of E, with elementary proofs. We give proofs of them without
using degree theory.