Generalized Weak Contractions Involving a Pair of Auxiliary Functions via Locally Transitive Binary Relations and Applications to Boundary Value Problems
Nidal H. E. Eljaneid,
Esmail Alshaban,
Adel Alatawi,
Montaser Saudi Ali,
Saud S. Alsharari,
Faizan Ahmad Khan
Affiliations
Nidal H. E. Eljaneid
Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia
Esmail Alshaban
Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia
Adel Alatawi
Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia
Montaser Saudi Ali
Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia
Saud S. Alsharari
Department of Mathematics, Science Faculty, Northern Border University, Arar 73213, Saudi Arabia
Faizan Ahmad Khan
Department of Mathematics, Science Faculty, University of Tabuk, Tabuk 71491, Saudi Arabia
The intent of this paper was to investigate the fixed-point results under relation-theoretic generalized weak contractivity condition employing a pair of auxiliary functions ϕ and ψ verifying appropriate properties. In proving our outcomes, we observed that the partial-ordered relation (even, transitive relation) adopted by earlier authors can be weakened to the extent of a locally ϝ-transitive binary relation. The findings proved herewith generalize, extend, improve, and unify a number of existing outcomes. To validate of our findings, we offer a number of illustrative examples. Our outcomes assist us to figure out the existence and uniqueness of solutions to a boundary value problem.
