Fixed point theory and its applications to real world problems

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FIXED POINT THEORYAND ITS APPLICATIONSTO REAL WORLD PROBLEMS FIXED POINT THEORYAND ITS APPLICATIONSTO REAL WORLD PROBLEMS CONTENTS PREFACE Chapter 1DYNAMICAL BEHAVIOR OF GENERALIZEDLOGISTIC MAPS USING SUPERIORFIXED-POINT FEEDBACK SYSTEM Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. DYNAMICS OF GENERALIZED LOGISTICMAPS USING SUPERIOR FIXED-POINTFEEDBACK SYSTEM 4. CHAOS IN GENERALIZED LOGISTIC MAPS USINGSUPERIOR FIXED-POINT FEEDBACK SYSTEM 4.1. Time-Series Analysis 4.2. Period-Doubling Bifurcation Analysis 5. LYAPUNOV EXPONENT IN GENERALIZEDLOGISTIC MAPS USING SUPERIORFIXED-POINT FEEDBACK SYSTEM CONCLUSION REFERENCES Chapter 2ON A NEW TYPE OF LIPSCHITZ MAPPINGPAIRS IN FIXED POINT CONSIDERATIONSAND APPLICATIONS Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS 3. APPLICATIONS REFERENCES Chapter 3 ON GEOMETRIC PROPERTIES OF NON-UNIQUE FIXED POINTS IN b-METRIC SPACES Abstract 1. INTRODUCTION 2. MAIN RESULTS 3. APPLICATION CONCLUSION REFERENCES Chapter 4FIXED POINT THEOREM FOR MULTIVALUEDMAPPINGS WITH RATIONAL EXPRESSIONSIN COMPLETE PARTIAL METRIC SPACES Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS ACKNOWLEDGMENT REFERENCES Chapter 5COMMON FIXED POINT THEOREMSIN MENGER PM-SPACES WITH NONLINEARGENERALIZED TYPE Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS ACKNOWLEDGMENTS REFERENCES Chapter 6COINCIDENCE POINT THEOREMS FORNON-EXPANSIVE TYPE MAPPINGS AND ANAPPLICATION TO DYNAMIC PROGRAMMING Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS 3. AN APPLICATION TO DYNAMIC PROGRAMMING REFERENCES Chapter 7 SOME STABILITY AND DATA DEPENDENCE RESULTS FOR PSEUDO-CONTRACTIVE MULTIVALUED MAPPINGS Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULT 3. STABILITY OF FIXED POINT SETS UNDERBOUNDED PROXIMAL CONVERGENCE ACKNOWLEDGMENTS REFERENCES Chapter 8MULTIVALUED GERAGHTY-CONTRACTIONS AND APPLICATIONS TOFRACTIONAL DIFFERENTIAL INCLUSIONS Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS 3. FIXED POINT ON A METRIC SPACES EQUIPPEDWITH A PARTIAL ORDERING 4. APPLICATION TO FRACTIONAL DIFFERENTIALINCLUSIONS REFERENCES Chapter 9NEAR-FIXED POINT, NEAR-FIXED INTERVALCIRCLE AND NEAR-FIXED INTERVAL DISCIN METRIC INTERVAL SPACE Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS 4. OPEN PROBLEM CONCLUSION REFERENCES Chapter 10APPLICATIONS OF GENERALIZED −´C IRI´CAND −BROWDER CONTRACTIONS INPARTIAL METRIC SPACES Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS 3. DISCONTINUOUS MAPS AS ACTIVATIONFUNCTIONS 4. APPLICATION CONCLUSION REFERENCES Chapter 11FIXED POINT THEOREMSFOR ASYMPTOTICALLY REGULARMAPS IN PARTIAL METRIC SPACES Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS 3. APPLICATION REFERENCES Chapter 12EXISTENCE OF COMMON FIXED POINTVIA QUASI-PARTIAL METRICWITH APPLICATIONS Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULTS 4. DISCUSSION ON QUASI PARTIAL METRIC SPACE 5. APPLICATION TO DYNAMICAL PROGRAMMING 6. APPLICATION TO SPRING MASS SYSTEM CONCLUSION REFERENCES Chapter 13AN ITERATIVE ALGORITHMFOR WEAK CONTRACTION MAPPINGS Abstract 1. INTRODUCTION 2. STABILITY 3. MAIN RESULTS 4. APPLICATION REFERENCES Chapter 14FIXED POINT STABILITY OF ADDITIVEFUNCTIONAL EQUATIONS IN PARANORMEDSPACES Abstract 1. INTRODUCTION AND PRELIMINARIES 2. FIXED POINT STABILITY OF FUNCTIONALEQUATIONS REFERENCES Chapter 15AMIABLE FIXED SETS AND THEIRDESCRIPTIVE PROXIMITIES:AN INTRODUCTION Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. SHAPE COMPLEXES AND THEIR BOUNDARYREGIONS 4. CYCLES AND THEIR ABELIAN GROUPREPRESENTATIONS 5. BETTI NUMBERS complexes.6. PROXIMALLY CONTINUOUS MAPS AND SPATIALLYAMIABLE FIXED 7. DESCRIPTIVE PROXIMALLY CONTINUOUS MAPSAND DESCRIPTIVE AMIABLE FIXED SETS ACKNOWLEDGMENTS REFERENCES Chapter 16STRONG COUPLED FIXED POINTS OFKANNAN TYPE AND REICH TYPE CYCLICCOUPLED MAPPINGS IN S-METRIC SPACES Abstract 1. INTRODUCTION AND PRELIMINARIES 2. STRONG COUPLED FIXED POINTS OF KANNANTYPE CYCLIC COUPLED MAPPINGS 3. STRONG COUPLED FIXED POINTS OF REICH TYPECYCLIC COUPLED MAPPINGS ACKNOWLEDGMENTS REFERENCES Chapter 17 A COMMON FIXED POINT THEOREM FOR A PAIR OF MAPPINGS IN FUZZY METRIC SPACES WITH AN APPLICATION Abstract 1. INTRODUCTION 2. PRELIMINARIES 3. MAIN RESULT 4. AN APPLICATION REFERENCES Chapter 18 COUPLED COMMON FIXED POINT THEOREMS FOR GERAGHTY CONTRACTION MAPPINGS SATISFYING MIXED WEAKLY MONOTONE PROPERTY IN Sb-METRIC SPACE Abstract 1. INTRODUCTION AND PRELIMINARIES 2. MAIN RESULTS CONCLUSION ACKNOWLEDGMENT REFERENCES Chapter 19FIXED POINT THEOREMS FORMULTIVALUED SUZUKI TYPEZ