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- Title
SEARCH OF MINIMAL METRIC STRUCTURE IN THE CONTEXT OF FIXED POINT THEOREM AND CORRESPONDING OPERATOR EQUATION PROBLEMS.
- Authors
SAVALIYA, JAYESH; GOPAL, DHANANJAY; SRIVASTAVA, SHAILESH KUMAR; RAKOČEVIČ, VLADIMIR
- Abstract
The paper contains a brief summary of the generalization of metrical structure regarding the fixed point theorem and corresponding operator equation problems. We observed that many researcher either tried to weaken the metrical structure, the contraction condition, or both. The idea behind this paper is to look for a minimal metrical structure to establish fixed point theorems. In this connection, we present new variants of the known fixed point theorem under non-triangular metric space (namely F-contraction, (A; S)-contraction, (A; S)-contraction). We also apply the obtain result in solving various types of operator equation problems. e.g., high-order fractional differential equation with non-local boundary conditions and non-linear integral equation problems.
- Subjects
OPERATOR equations; CONTRACTIONS (Topology); FIXED point theory; NONLINEAR integral equations; BOUNDARY value problems; FRACTIONAL differential equations; METRIC spaces
- Publication
Fixed Point Theory, 2024, Vol 25, Issue 1, p379
- ISSN
1583-5022
- Publication type
Article
- DOI
10.24193/fpt-ro.2024.1.24