Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

[EN] In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond-Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.Dubey, R.; Mishra, LN.; Sánchez Ruiz, LM. (2019). Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry (Basel). 11(11):1-18. https://doi.org/10.3390/sym11111348S118111

Nondifferentiable multiobjective programming problem under strongly K-Gf-pseudoinvexity assumptions

[EN] In this paper we consider the introduction of the concept of (strongly) K-G(f)-pseudoinvex functions which enable to study a pair of nondifferentiable K-G- Mond-Weir type symmetric multiobjective programming model under such assumptions.Dubey, R.; Mishra, LN.; Sánchez Ruiz, LM.; Sarwe, DU. (2020). Nondifferentiable multiobjective programming problem under strongly K-Gf-pseudoinvexity assumptions. Mathematics. 8(5):1-11. https://doi.org/10.3390/math8050738S11185Antczak, T. (2007). New optimality conditions and duality results of type in differentiable mathematical programming. Nonlinear Analysis: Theory, Methods & Applications, 66(7), 1617-1632. doi:10.1016/j.na.2006.02.013Antczak, T. (2008). On G-invex multiobjective programming. Part I. Optimality. Journal of Global Optimization, 43(1), 97-109. doi:10.1007/s10898-008-9299-5Ferrara, M., & Viorica-Stefanescu, M. (2008). Optimality conditions and duality in multiobjective programming with invexity. YUJOR, 18(2), 153-165. doi:10.2298/yjor0802153fChen, X. (2004). Higher-order symmetric duality in nondifferentiable multiobjective programming problems. Journal of Mathematical Analysis and Applications, 290(2), 423-435. doi:10.1016/j.jmaa.2003.10.004Long, X. (2013). Sufficiency and duality for nonsmooth multiobjective programming problems involving generalized univex functions. Journal of Systems Science and Complexity, 26(6), 1002-1018. doi:10.1007/s11424-013-1089-6Dubey, R., Mishra, L. N., & Sánchez Ruiz, L. M. (2019). Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry, 11(11), 1348. doi:10.3390/sym11111348Pitea, A., & Postolache, M. (2011). Duality theorems for a new class of multitime multiobjective variational problems. Journal of Global Optimization, 54(1), 47-58. doi:10.1007/s10898-011-9740-zPitea, A., & Antczak, T. (2014). Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems. Journal of Inequalities and Applications, 2014(1). doi:10.1186/1029-242x-2014-333Dubey, R., Deepmala, & Narayan Mishra, V. (2020). Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints. Statistics, Optimization & Information Computing, 8(1), 187-205. doi:10.19139/soic-2310-5070-60

Generalized Second-Order G-Wolfe Type Fractional Symmetric Program and their Duality Relations under Generalized Assumptions

In this article, we formulate the concept of generalize bonvexity/pseudobonvexity functions. We formulate duality results for second-order fractional symmetric dual programs of G-Wolfe-type model. In the next section, we explain the duality theorems under generalize bonvexity/pseudobonvexity assumptions. We identify a function lying exclusively in the class of generalize pseudobonvex and not in class of generalize bonvex functions. Our results are more generalized several known results in the literature

महिषासुर: मिथक व परंपराएं

इक्कसवीं सदी के दूसरे दशक में भारत में महिषासुर आंदोलन द्विज संस्कृति के लिए चुनौती बनकर उभरा। इसके माध्यम से आदिवासियों, पिछड़ों और दलितों के एक बड़े हिस्से ने अपनी सांस्कृतिक दावेदारी पेश की। लेकिन यह आंदोलन क्या है, इसकी जड़ें समाज में कहां तक फैली हैं, बहुजनों की सांस्कृतिक परंपरा में इसका क्या स्थान है, मौजूदा लोक-जीवन में महिषासुर की उपस्थिति किन-किन रूपों में है, इसके पुरातात्विक साक्ष्य क्या हैं? गीतों-कविताओं व नाटकों में महिषासुर किस रूप में याद किए जा रहे हैं और अकादमिक-बौद्धिक वर्ग को इस आंदोलन ने किस रूप में प्रभावित किया है, उनकी प्रतिक्रियाएं क्या हैं? आदि प्रश्नों पर विमर्श हमें एक ऐसी बौद्धिक यात्रा की ओर ले जाने में सक्षम हैं, जिससे हममें अधिकांश अभी तक अपरिचित रहे हैं। क्या महिषासुर दक्षिण एशिया के अनार्यों के पूर्वज थे, जो बाद में एक मिथकीय चरित्र बन कर बहुजन संस्कृति के प्रतीक पुरुष बन गए? क्या यह बहुत बाद की परिघटना है, जब माकण्डेय पुराण, दुर्गासप्तशती जैसे ग्रंथ रच कर, एक कपोल-कल्पित देवी के हाथों महिषासुर की हत्या की कहानी गढ़ी गई? इस आंदोलन की सैद्धांतिकी क्या है? प्रमोद रंजन द्वारा संपादित किताब “महिषासुर: मिथक व परंपराएं” में लेखकों ने उपरोक्त प्रश्नों पर विचार किया है तथा विलुप्ति के कगार पर खड़े असुर समुदाय का विस्तृत नृवंशशास्त्रीय अध्ययन भी प्रस्तुत किया है। इस पुस्तक में समकालीन भारतीय साहित्य में महिषासुर पर लिखी गई कविताओं व गीतों का प्रतिनिधि संकलन भी है तथा महिषासुर की बहुजन कथा पर आधारित एक नाटक भी प्रकाशित है। समाज-विज्ञान व सांस्कृतिक विमर्श के अध्येताओं, सामाजिक-राजनीतिक कार्यकर्ताओं, साहित्य प्रेमियों के लिए यह एक आवश्यक पुस्तक है

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

In this article, we study the existence of Gf-bonvex/Gf -pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions

Duality for Unified Higher-Order Minimax Fractional Programming with Support Function under Type-I Assumptions

This article is devoted to discussing the nondifferentiable minimax fractional programming problem with type-I functions. We focus our study on a nondifferentiable minimax fractional programming problem and formulate a higher-order dual model. Next, we establish weak, strong, and strict converse duality theorems under generalized higher-order strictly pseudo ( V , α , ρ , d ) -type-I functions. In the final section, we turn our focus to study a nondifferentiable unified minimax fractional programming problem and the results obtained in this paper naturally unify. Further, we extend some previously known results on nondifferentiable minimax fractional programming in the literature

New Class of K-G-Type Symmetric Second Order Vector Optimization Problem

In this paper, we present meanings of K-Gf-bonvexity/K-Gf-pseudobonvexity and their generalization between the above-notice functions. We also construct various concrete non-trivial examples for existing these types of functions. We formulate K-Gf-Wolfe type multiobjective second-order symmetric duality model with cone objective as well as cone constraints and duality theorems have been established under these aforesaid conditions. Further, we have validates the weak duality theorem under those assumptions. Our results are more generalized than previous known results in the literature

A class of second order nondifferentiable symmetric duality relations under generalized assumptions

In this article, a pair of second-order nondifferentiable symmetric dual model in optimization problem is formulated over arbitrary cones. For a differentiable function, we consider the definition of strongly K-pseudobonvexity convexity. Next, we derive the appropriate duality results under aforesaid assumptions

Modeling of Diffusive Patterns in Predator–Prey System using Turing Instability and Amplitude Equations

In this work, we have investigated the evolution of diffusive pattern formation in a predator–prey model under type-III functional response. Using stability analysis, we receive the significant specifications for Turing instability (diffusive-driven instability), and with the help of these conditions, recognize the corresponding realm in the region of interest. Moreover, we present a qualitative analysis of growth and development actions that involves species distribution and their interplay of the spatially distributed populace with diffusion and obtain the conditions for spatial patterns like spots, spot-stripe, and stripes. Using weakly nonlinear analysis, we derive the equations of amplitude for slow modulation near the Turing boundary. By the series of numerical simulations, we receive intricate spatial patterns, particularly spot, stripe, and spot-stripe in the Turing realm. The consequences of this paper are general in the real world and can be used to investigate the impact of self-diffusion on other predator–prey systems. It will improve our understanding to understand the dynamical behavior of realistic models

A class of new type unified non-differentiable higher order symmetric duality theorems over arbitrary cones under generalized assumptions

In the present paper, a newly combined higher-order non-differentiable symmetric duality in scalar-objective programming over arbitrary cones is formulated. In literature we have discussed primal-dual results with arbitrary cones, while in this article, we have derived combined result with one model over arbitrary cones. The theorems of duality are derived for these problems under η-pseudoinvexity/η-invexity/C-pseudoconvexity/C-convexity speculations over arbitrary cones