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 (Mathematics)
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 <semantics>ϕ</semantics> and <semantics>ψ</semantics> 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 <semantics>ϝ</semantics>-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.