This book provides a primary resource in basic fixed-point theorems due to Banach, Brouwer, Schauder and Tarski and their applications.

Contraction principle is provided with two proofs: one due to Palais and the other due to Barranga. Applications of the contraction principle include the proofs of algebraic Weierstrass preparation theorem, a Cauchy—Kowalevsky theorem for partial differential equations and the central limit theorem.

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Subba Rao. His areas of interest include classical analysis, nonlinear analysis and fixed-point theory, fuzzy- set theory, functional equations and mathematics education. He has published over 70 papers and served on the editorial board of the Journal of Analysis and the Journal of Differential Equations and Dynamical Systems. He received an award for his outstanding contributions to mathematical sciences in and the Lifetime Achievement Award from the FIM in He has given various invited talks at international conferences and completed brief visiting assignments in many countries such as Canada, Czech Republic, Germany, Greece, Japan, Slovak Republic and the USA.

JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Analysis. Forum for Interdisciplinary Mathematics Free Preview. Buy eBook. The existence and uniqueness of a random solution for nonlinear integral equation is established using this contractive operator. National Center for Biotechnology Information , U. Journal List Heliyon v. Published online May Author information Article notes Copyright and License information Disclaimer.

Department of Mathematics, Covenant University, P.

## Provability Logic

Kanayo Stella Eke: gn. Abstract This particular research establishes some random fixed point theorems for general nonlinear random contractive operators in the context of partially ordered separable metric spaces.

Rodriguez-Lopez [9] proved their theorem using Banach contraction mappings while we proved our theorems using Hardy and Rogers contraction mappings. Keyword: Applied mathematics. Introduction F ixed point theory plays very fundamental role in solving deterministic operator equations.

Definition 1. Results This section proves the existence and uniqueness of random fixed point for contractive mappings in partially ordered separable metric spaces. Example 3. Remark 3. Corollary 3. Discussion The theory of random nonlinear integral equations play a significant role in modeling physical phenomena in various branches of mathematics and applied sciences.

Definition 4. Lemma 4. Theorem 4. Conclusion This research proved the existence and uniqueness of random fixed point for certain contractive mappings in complete partially ordered separable metric spaces. Declarations Author contribution statement K. Eke; Wrote the paper. Akewe; Conceived and designed the experiment. Bishop; Analyzed and interpreted the data.

### Fixed Point Theorems

Funding statement This work was supported by Covenant University. Competing interest statement The authors declare no conflict of interest. Additional information No additional information is available for this paper. References 1. Banach S. Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Ran A. Rashwan R. Rashwan and D. Albaqeri, A common fixed point theorem and application to random integral equations.

Hans O. Random fixed point theorems; pp. Hans, Random fixed point theorems. Information Theory. Randon fixed point approximation by differentiable trajectories; pp.

## Some Fixed Point Theorems in Pseudo Multiplicative Metric Spaces with Convex Structure

Hans and A. Randon fixed point approximation by differentiable trajectories. In: Trans. Information Theory, pp Okeke G. Convergence and almost sure T-stability for random Noor-type iterative scheme.

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Pure Appl. Okeke and K. Lee C. On random nonlinear contractions. Lee and W.

Systems Theory, Vol. Saluja G. Some common random fixed point theorems for contractive type conditions in cone random metric spaces.

## Fixed point theorems on fuzzy metric spaces - IEEE Conference Publication

Acta Univ. Sapientiae, Math. Saluja and B. Sapientiae, Mathematica, Vol. Nieto J. Random fixed point theorems in partially ordered metric spaces. Fixed Point Theory Appl.