{"title":"Fs−CONTRACTIVE MAPPINGS IN CONTROLLED METRIC TYPE SPACES","authors":"D. Rizk","doi":"10.53006/RNA.928319","DOIUrl":"https://doi.org/10.53006/RNA.928319","url":null,"abstract":"","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45317433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some common fixed-point theorems for a pair of p-hybrid mappings via common limit range property in G-metric space","authors":"Lucas Wangwe, Santosh Kumar","doi":"10.53006/RNA.907704","DOIUrl":"https://doi.org/10.53006/RNA.907704","url":null,"abstract":"","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44908502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On pricing variance swaps in discretely-sampled with High Volatility model","authors":"Youssef El-Khatib, M. Alshamsi, Jun Fan","doi":"10.53006/RNA.908113","DOIUrl":"https://doi.org/10.53006/RNA.908113","url":null,"abstract":"","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47652490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1923 S. Lefschetz proved the famous xed point theorem known as the Lefschetz xed point theorem (comp. [5], [9], [20], [21]. The multivalued case was considered for the rst time in 1946 by S. Eilenberg and D. Montgomery ([10]). They proved the Lefschetz xed point theorem for acyclic mappings of compact ANR-spaces (absolute neighbourhood retracts (see [4] or [13]) using Vietoris mapping theorem (see [4], [13], [16]) as a main tool. In 1970 Eilenberg, Montgomery's result was generalized for acyclic mappings of complete ANR-s (see [17]). Next, a class of admissible multivalued mappings was introduced ([13] or [16]). Note that the class of admissible mappings is quite large and contains as a special case not only acyclic mappings but also nite compositions of acyclic mappings. For this class of multivalued mappings several versions of the Lefschetz xed point theorem was proved (comp. [11], [13] [15], [18], [19], [27]). In 1982 G. Skordev and W. Siegberg ([26]) introduced the class of multivalued mappings so-called now (1 − n)-acyclic mappings. Note that the class (1 − n)-acyclic mappings contains as a special case n-valued mappings considered in [6], [12], [28]. We recommend [8] for the most important results connected with (1 − n)-acyclic mappings. Finally, the Lefschetz xed point theorem was considered for spheric mappings (comp. [3], [2], [7], [23]) and for random multivalued mappings (comp. [1], [2], [13]). Let us remark that the main classes of spaces for which the Lefschetz xed point theorem was formulated are the class of ANR-spaces ([4]) and MANR-spaces (multi absolute neighbourhood retracts (see [27]). The aim of this paper is to recall the most important results concerning the Lefschetz xed point theorem for multivalued mappings and to prove new versions of this theorem, mainly for AANR-spaces (approximative absolute neighborhood retracts (see [4] or [13]) and for MANR-s. We believe that this article will be useful for analysts applying topological xed point theory for multivalued mappings in nonlinear analysis, especially in di erential inclusions. Email address: gorn@mat.umk.pl (Lech Górniewicz) Received March 17, 2021, 2021, Accepted May 14, 2021, Online May 22, 2021. L. Górniewicz, Results in Nonlinear Anal. 4 (2021), 116 126 117
{"title":"Recent advances in the Lefschetz fixed point theory for multivalued mappings","authors":"L. Górniewicz","doi":"10.53006/RNA.941060","DOIUrl":"https://doi.org/10.53006/RNA.941060","url":null,"abstract":"In 1923 S. Lefschetz proved the famous xed point theorem known as the Lefschetz xed point theorem (comp. [5], [9], [20], [21]. The multivalued case was considered for the rst time in 1946 by S. Eilenberg and D. Montgomery ([10]). They proved the Lefschetz xed point theorem for acyclic mappings of compact ANR-spaces (absolute neighbourhood retracts (see [4] or [13]) using Vietoris mapping theorem (see [4], [13], [16]) as a main tool. In 1970 Eilenberg, Montgomery's result was generalized for acyclic mappings of complete ANR-s (see [17]). Next, a class of admissible multivalued mappings was introduced ([13] or [16]). Note that the class of admissible mappings is quite large and contains as a special case not only acyclic mappings but also nite compositions of acyclic mappings. For this class of multivalued mappings several versions of the Lefschetz xed point theorem was proved (comp. [11], [13] [15], [18], [19], [27]). In 1982 G. Skordev and W. Siegberg ([26]) introduced the class of multivalued mappings so-called now (1 − n)-acyclic mappings. Note that the class (1 − n)-acyclic mappings contains as a special case n-valued mappings considered in [6], [12], [28]. We recommend [8] for the most important results connected with (1 − n)-acyclic mappings. Finally, the Lefschetz xed point theorem was considered for spheric mappings (comp. [3], [2], [7], [23]) and for random multivalued mappings (comp. [1], [2], [13]). Let us remark that the main classes of spaces for which the Lefschetz xed point theorem was formulated are the class of ANR-spaces ([4]) and MANR-spaces (multi absolute neighbourhood retracts (see [27]). The aim of this paper is to recall the most important results concerning the Lefschetz xed point theorem for multivalued mappings and to prove new versions of this theorem, mainly for AANR-spaces (approximative absolute neighborhood retracts (see [4] or [13]) and for MANR-s. We believe that this article will be useful for analysts applying topological xed point theory for multivalued mappings in nonlinear analysis, especially in di erential inclusions. Email address: gorn@mat.umk.pl (Lech Górniewicz) Received March 17, 2021, 2021, Accepted May 14, 2021, Online May 22, 2021. L. Górniewicz, Results in Nonlinear Anal. 4 (2021), 116 126 117","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48137042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we investigate the asymptotic stability of the zero solution for Caputo-Hadamard fractional dynamic equations on a time scale. We will make use of the Krasnoselskii fixed point theorem in a weighted Banach space to show new stability results.
{"title":"Asymptotic stability in Caputo-Hadamard fractional dynamic equations","authors":"A. Ardjouni","doi":"10.53006/RNA.865900","DOIUrl":"https://doi.org/10.53006/RNA.865900","url":null,"abstract":"In this work, we investigate the asymptotic stability of the zero solution for Caputo-Hadamard fractional dynamic equations on a time scale. We will make use of the Krasnoselskii fixed point theorem in a weighted Banach space to show new stability results.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45069394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we obtain the general solutions of a sum form functional equation arising from the expected value of a discrete random variable. The signi(cid:28)cance of its general solutions in reference to entropies emerging from information theory and diversity index has been discussed.
{"title":"On a sum form functional equation emerging from statistics and its applications","authors":"D. Singh, Shveta Grover","doi":"10.53006/RNA.843040","DOIUrl":"https://doi.org/10.53006/RNA.843040","url":null,"abstract":"In this paper, we obtain the general solutions of a sum form functional equation arising from the expected value of a discrete random variable. The signi(cid:28)cance of its general solutions in reference to entropies emerging from information theory and diversity index has been discussed.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42918846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A fixed point theorem without a Picard operator","authors":"E. Karapınar","doi":"10.53006/rna.904880","DOIUrl":"https://doi.org/10.53006/rna.904880","url":null,"abstract":"In this short note, we propose a fixed point theorem in the setting of a Banach space without using a Picard operator.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45830739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .
{"title":"The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings","authors":"Linxin Li, Ding-Ping Wu","doi":"10.53006/RNA.793940","DOIUrl":"https://doi.org/10.53006/RNA.793940","url":null,"abstract":"Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42205423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1994, Llinares introduced mc-spaces and began to study KKM theoretic results on them. Since 1998, he became an L-space theorist and repeated to claim that his mc-spaces generalize G-convex spaces without any justifications. Later he insisted that his mc-spaces are the same as L-spaces. Hence his study on mc-spaces is useless now as the L-space case shown by our previous works. The present article is a continuation of our previous works on L-spaces and concerns with the rise and fall of mc-spaces. This paper will be an important record for the history of the KKM theory.
{"title":"The rise and fall of MC-spaces","authors":"Sehie Park","doi":"10.53006/RNA.852462","DOIUrl":"https://doi.org/10.53006/RNA.852462","url":null,"abstract":"In 1994, Llinares introduced mc-spaces and began to study KKM theoretic results on them. Since 1998, he became an L-space theorist and repeated to claim that his mc-spaces generalize G-convex spaces without any justifications. Later he insisted that his mc-spaces are the same as L-spaces. Hence his study on mc-spaces is useless now as the L-space case shown by our previous works. The present article is a continuation of our previous works on L-spaces and concerns with the rise and fall of mc-spaces. This paper will be an important record for the history of the KKM theory.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45896968","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper is devoted to extension of Synge equations describing motion of two mass charged particles in the frame of classical relativistic electrodynamics including radiation terms and spin equations. In previous papers we have derived equations of motion just with radiation terms. Our radiation terms correspond to the Dirac physical assumptions but they differ from Dirac’s terms on the mathematical derivation. They generate neutral type equations of motion with both retarded and advanced arguments. Here we consider two-body problem with spin following the Corben’s technique. As in the original Synge model the number of the spin equations is more than the number of the unknown functions. We prove that six spin equations are a consequence of the rest ones and in this manner we obtain six equations for the six unknown spin functions. This consequence is in weak sense obtained by scalar multiplication.
{"title":"Spin Three-Body Problem of Classical Electrodynamics with Radiation Terms (I) Derivation of Spin Equations","authors":"V. Angelov","doi":"10.53006/RNA.833345","DOIUrl":"https://doi.org/10.53006/RNA.833345","url":null,"abstract":"The paper is devoted to extension of Synge equations describing motion of two mass charged particles in the frame of classical relativistic electrodynamics including radiation terms and spin equations. In previous papers we have derived equations of motion just with radiation terms. Our radiation terms correspond to the Dirac physical assumptions but they differ from Dirac’s terms on the mathematical derivation. They generate neutral type equations of motion with both retarded and advanced arguments. Here we consider two-body problem with spin following the Corben’s technique. As in the original Synge model the number of the spin equations is more than the number of the unknown functions. We prove that six spin equations are a consequence of the rest ones and in this manner we obtain six equations for the six unknown spin functions. This consequence is in weak sense obtained by scalar multiplication.","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46644850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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