Let f be a transcendental meromorphic function defined in the complex plane C and k ? N. We consider the value distribution of the differential polynomial fq0(f(k))qk, where q0(?2), qk(?1) are integers. We obtain a quantitative estimation of the characteristic function T(r,f) in terms of N?(r, 1/fq0(f(k))qk-1). Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., Vol. 14, PP. 93-100, 2011); Karmakar and Sahoo (Results Math., Vol. 73, 2018) for a particular class of transcendental meromorphic functions.

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This paper proposes a moth-dolphin based nature inspired optimization algorithm. This algorithm embeds the communication behavior of dolphin to Moth. The Moth route towards moon through the moon light in an optimized manner. But each moth doesn’t follow optimized path to travel towards the moon. The communication among the moth enables them to follow the best path towards moon. Thus, moth-dolphin algorithm uses the communication between moths to enhance the performance. The Moth–dolphin is an optimization algorithm which uses the exploration as well as exploitation search to achieve the global optima. The performance comparison of proposed algorithm with the moth-flame optimization algorithm, modified particle swarm optimization algorithm, differential evaluation and non-dominated sorting genetic algorithm over unimodal as well as multimodal functions ensures better results

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