Coupled fixed points of -contractive mappings in partially ordered b-metric spaces

Area of Science:

• Fixed-point theory
• Nonlinear analysis
• Metric spaces

Background:

• Fixed-point theory is crucial for solving equations in various scientific fields.
• Generalized contractions and altering distance functions are advanced concepts in metric space analysis.
• Ordered metric spaces provide a framework for studying ordered structures within metric spaces.

Purpose of the Study:

• To establish the existence and uniqueness of fixed points for self-mappings in ordered metric type spaces.
• To investigate self-mappings that satisfy generalized contraction conditions utilizing altering distance functions.
• To extend and generalize existing theorems in fixed-point theory.

Main Methods:

• Utilizing concepts of ordered metric type spaces.
• Applying generalized contraction mappings involving altering distance functions.
• Proving existence and uniqueness theorems for fixed points.

Main Results:

• The existence and uniqueness of fixed points are demonstrated for the specified self-mappings.
• The established results extend and generalize several known theorems in the field.
• Illustrative examples are provided to validate the theoretical outcomes.

Conclusions:

• The study successfully proves the existence and uniqueness of fixed points under the given conditions.
• The findings contribute to the advancement of fixed-point theory, particularly in ordered metric spaces.
• The research offers a generalized framework for analyzing contraction mappings.