Fixed Point Theorems for Integral Type Mappings under b-(E.A.) Property in b-metric Spaces
Sunaina Jain *
Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, India.
Ranbir Singh
Department of Physical Science(Mathematics), Baba Mastnath University, Asthal Bohar, Rohtak, India.
Poonam
Department of Mathematics, Govt. College for Women, Jassaur Kheri, Jhajjar, India.
*Author to whom correspondence should be addressed.
Abstract
This paper studies the existence and uniqueness of fixed points for a class of Lebesgue integrable self-mappings satisfying a generalized b-(E.A.) property in the setting of b-metric spaces. Motivated by recent advances in fixed point theory in generalized metric structures, we establish new integral type contraction conditions that guarantee the existence of a unique fixed point in complete b-metric spaces.
The convergence of the associated Picard iteration is proved using the intrinsic properties of b-metrics, and the uniqueness of the fixed point follows without requiring additional continuity assumptions on the mappings. Moreover, we discuss the well-posedness of the fixed-point problem in the sense that the fixed point is uniquely determined and stable under convergence in the b-metric framework.
Keywords: b-Metric spaces, cauchy sequence, contractive mapping, fixed point theorems